{"quality_controlled":"1","doi":"10.1145/2261250.2261287","year":"2012","day":"20","_id":"3133","page":"249 - 258","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","title":"Alexander duality for functions: The persistent behavior of land and water and shore","date_created":"2018-12-11T12:01:35Z","date_updated":"2021-01-12T07:41:17Z","language":[{"iso":"eng"}],"author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert"},{"full_name":"Kerber, Michael","last_name":"Kerber","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8030-9299","first_name":"Michael"}],"acknowledgement":"his research is partially supported by the National Science Foundation (NSF) under grant DBI-0820624, the European Science Foundation under the Research Networking Programme, and the Russian Government Project 11.G34.31.0053.\r\nThe authors thank an anonymous referee for suggesting the simplified proof of the Contravariant PE Theorem given in this paper. They also thank Frederick Cohen, Yuriy Mileyko and Amit Patel for helpful discussions.","conference":{"location":"Chapel Hill, NC, USA","start_date":"2012-06-17","end_date":"2012-06-20","name":"SCG: Symposium on Computational Geometry"},"date_published":"2012-06-20T00:00:00Z","oa_version":"Preprint","oa":1,"status":"public","abstract":[{"lang":"eng","text":"This note contributes to the point calculus of persistent homology by extending Alexander duality from spaces to real-valued functions. Given a perfect Morse function f: S n+1 →[0, 1 and a decomposition S n+1 = U ∪ V into two (n + 1)-manifolds with common boundary M, we prove elementary relationships between the persistence diagrams of f restricted to U, to V, and to M. "}],"department":[{"_id":"HeEd"}],"publication":"Proceedings of the twenty-eighth annual symposium on Computational geometry ","month":"06","citation":{"short":"H. Edelsbrunner, M. Kerber, in:, Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry , ACM, 2012, pp. 249–258.","ieee":"H. Edelsbrunner and M. Kerber, “Alexander duality for functions: The persistent behavior of land and water and shore,” in <i>Proceedings of the twenty-eighth annual symposium on Computational geometry </i>, Chapel Hill, NC, USA, 2012, pp. 249–258.","chicago":"Edelsbrunner, Herbert, and Michael Kerber. “Alexander Duality for Functions: The Persistent Behavior of Land and Water and Shore.” In <i>Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry </i>, 249–58. ACM, 2012. <a href=\"https://doi.org/10.1145/2261250.2261287\">https://doi.org/10.1145/2261250.2261287</a>.","ama":"Edelsbrunner H, Kerber M. Alexander duality for functions: The persistent behavior of land and water and shore. In: <i>Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry </i>. ACM; 2012:249-258. doi:<a href=\"https://doi.org/10.1145/2261250.2261287\">10.1145/2261250.2261287</a>","apa":"Edelsbrunner, H., &#38; Kerber, M. (2012). Alexander duality for functions: The persistent behavior of land and water and shore. In <i>Proceedings of the twenty-eighth annual symposium on Computational geometry </i> (pp. 249–258). Chapel Hill, NC, USA: ACM. <a href=\"https://doi.org/10.1145/2261250.2261287\">https://doi.org/10.1145/2261250.2261287</a>","mla":"Edelsbrunner, Herbert, and Michael Kerber. “Alexander Duality for Functions: The Persistent Behavior of Land and Water and Shore.” <i>Proceedings of the Twenty-Eighth Annual Symposium on Computational Geometry </i>, ACM, 2012, pp. 249–58, doi:<a href=\"https://doi.org/10.1145/2261250.2261287\">10.1145/2261250.2261287</a>.","ista":"Edelsbrunner H, Kerber M. 2012. Alexander duality for functions: The persistent behavior of land and water and shore. Proceedings of the twenty-eighth annual symposium on Computational geometry . SCG: Symposium on Computational Geometry, 249–258."},"publisher":"ACM","scopus_import":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1109.5052"}],"publication_status":"published","type":"conference","publist_id":"3564"}